Recursive estimation of transition probabilities for jump Markov linear systems under minimum Kullback–Leibler divergence criterion

To reduce the computational complexity of the well-established recursive Kullback-Leibler (RKL) method for real-time applications, a recursive estimation method of the unknown transition probabilities (TPs) for the jump Markov linear system (JMLS) is developed in this study. The authors first explore an underlying idea that the RKL estimate of a diagonally dominant TP matrix (TPM) can be constructed by the estimate of each row vector of the TPM under the minimum K-L divergence criterion using observations at specific time steps. A modified derivation of the numerical solution to the RKL estimate that can avoid redundant likelihood computations is then exploited to estimate the specific row vector of the TPM per time step. The developed TP estimation method is computationally more efficient than either the RKL method or the maximum likelihood method, in particular for the JMLS defined over a high-dimensional state space or a multi-dimensional model space. The effectiveness of the developed TP estimation method is verified through a numerical example.